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Train Problems Practice Questions with Detailed Solutions – Level 3

Hard train problems on same and opposite direction crossings, trains fully inside tunnels, meeting points for trains that start at different times and the square-root rule for speeds.

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Questions, answer key and solutions.

Questions
50
Duration
75 min
Marks
50

Negative marking

Attempts
100
Access
Free
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Normal practice, or a Simulated test

Both use the same questions. Normal practice is untimed and needs no account: choose an option and the answer and solution appear at once. The Simulated test is the real computer-based format, with one 75-minute clock, a question palette and full screen, and your score, the key and the solutions arrive when you submit.

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The computer-based test format: one clock, a question palette, and a score the moment you submit.

  • A clock that does not pause. 75 minutes from the moment you begin, and the paper is submitted for you when it reaches zero.
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  • Full screen, proctored. The test takes over the screen; leaving it three times submits the paper.
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About this test

Train Problems Level 3 Practice Quiz on Crossings, Tunnels and Meeting Times

Aspirants who already know the basic train formulas can use this Level 3 Train Problems practice quiz on Aptitude360 to work through the harder side of the topic. It covers crossings in the same and opposite directions, trains passing platforms, bridges and tunnels, and trains that start at different times. Every question has a worked solution.

What this Level 3 train problems set tests

  • Finding speeds and lengths when two trains cross each other in the same and opposite directions
  • Trains passing men, joggers or cyclists moving with or against the train
  • Working out a train's length from pole, platform and bridge crossing times
  • Time for which a train is entirely inside a tunnel
  • Meeting time and place for trains leaving stations at different times
  • Speed ratios from the times taken after two trains meet
  • A passenger seated in one train timing another train on a parallel track

Key formulas for train problems

  • Unit change: \( 1\ \text{km/h}=\dfrac{5}{18}\ \text{m/s} \)
  • Opposite directions: \( t=\dfrac{L_{1}+L_{2}}{S_{1}+S_{2}} \)
  • Same direction (\( S_{1}>S_{2} \)): \( t=\dfrac{L_{1}+L_{2}}{S_{1}-S_{2}} \)
  • Fully inside a tunnel: \( t=\dfrac{L_{\text{tunnel}}-L_{\text{train}}}{S} \)
  • After meeting: \( \dfrac{S_{1}}{S_{2}}=\sqrt{\dfrac{t_{2}}{t_{1}}} \)

How to revise tough train questions

  • Convert every speed into metres per second before using lengths in metres
  • Treat a man, pole or tree as having zero length, but keep the man's own speed in the relative speed
  • When trains start at different times, first find the distance covered by the earlier train, then use relative speed
  • Distinguish between a train passing completely through a tunnel and being fully inside it

Who this practice set is for

Best suited to students at the advanced stage of arithmetic preparation who have finished the basics of speed, time and distance.

FAQs about Train Problems Practice Questions with Detailed Solutions – Level 3

What is the formula for a train crossing a pole?
Time equals the length of the train divided by its speed, because a pole is treated as a point. For a platform, add the platform's length to the train's length.
How do you find the time for two trains crossing each other?
Divide the sum of their lengths by the relative speed. Add the speeds if they move in opposite directions and subtract the slower speed from the faster one if they move in the same direction.
How to find the length of a train from platform crossing times?
While crossing a platform, a train covers its own length plus the platform's length. Equate this distance to speed multiplied by time and solve for the train's length.
What is the square root rule in train problems?
If two trains start together towards each other and take times t1 and t2 to reach their destinations after meeting, the ratio of their speeds equals the square root of t2 divided by t1.

Test structure

How the paper is split, and how long each part runs. A section you have finished cannot be returned to.

SectionQuestionsTime
Train Problems Level 35075 min

Marking & rules

Total marks
50 across 50 questions.
Negative marking
A wrong answer costs marks. Leaving a question unanswered costs nothing.
Attempts
100 in total. An attempt is spent the moment you begin one.

What you get when you submit

The analysis is ready the moment you submit the paper.

Score and accuracy

Marks, percentage, right, wrong and skipped, and the time you took.

Section by section

The same figures for each section, so a weak one cannot hide in an average.

The full answer key

Every question with your answer, the right one, the working, and the video where there is one.

Where you stand

Your score against the spread of everyone else who has sat this test.

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